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10.0

Apr 27, 2018
04/18

by
Bachmann, Friedrich, 1909-;Schmidt, Eckart, author

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xii, 191 pages : 25 cm

Topics: Polygons, Set theory, Polygons, Set theory, Algebraische Struktur, Lineare Algebra, Polygon, Polygon

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254

Jul 5, 2008
07/08

by
Benjamin Peirce

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Book digitized by Google from the library of Harvard University and uploaded to the Internet Archive by user tpb.

Topics: equal, angle, angles, sides, triangle, perpendicular, triangles, parallel, polygon, arc, regular...

Source: http://books.google.com/books?id=-iIAAAAAYAAJ&oe=UTF-8

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318

Aug 4, 2008
08/08

by
Benjamin Peirce

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Book digitized by Google from the library of Harvard University and uploaded to the Internet Archive by user tpb.

Topics: equal, angle, angles, sides, perpendicular, triangles, triangle, parallel, polygon, plane,...

Source: http://books.google.com/books?id=2iUAAAAAYAAJ&oe=UTF-8

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216

Jun 21, 2009
06/09

by
Benjamin Peirce

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Book digitized by Google from the library of Harvard University and uploaded to the Internet Archive by user tpb.

Topics: equal, angle, angles, sides, triangles, perpendicular, triangle, parallel, infinitely small,...

Source: http://books.google.com/books?id=pGILAAAAYAAJ&oe=UTF-8

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317

Oct 14, 2008
10/08

by
Benjamin Peirce

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Book digitized by Google from the library of the New York Public Library and uploaded to the Internet Archive by user tpb.

Topics: equal, angle, angles, sides, triangle, triangles, perpendicular, polygon, parallel, plane,...

Source: http://books.google.com/books?id=znkAAAAAMAAJ&oe=UTF-8

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542

Sep 26, 2008
09/08

by
Benjamin Peirce

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Book digitized by Google from the library of the New York Public Library and uploaded to the Internet Archive by user tpb.

Topics: equal, angle, angles, sides, triangle, triangles, perpendicular, parallel, polygon, plane, regular...

Source: http://books.google.com/books?id=_ogAAAAAMAAJ&oe=UTF-8

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429

Aug 30, 2008
08/08

by
Benjamin Peirce

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Book digitized by Google from the library of the University of Michigan and uploaded to the Internet Archive by user tpb.

Topics: equal, angle, angles, sides, perpendicular, triangle, triangles, parallel, polygon, arc, regular...

Source: http://books.google.com/books?id=Lt02AAAAMAAJ&oe=UTF-8

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Aug 7, 2008
08/08

by
Benjamin Peirce

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Book digitized by Google from the library of Harvard University and uploaded to the Internet Archive by user tpb.

Topics: equal, angle, angles, sides, perpendicular, triangle, triangles, polygon, parallel, plane,...

Source: http://books.google.com/books?id=ZyYAAAAAYAAJ&oe=UTF-8

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Sep 26, 2008
09/08

by
Benjamin Peirce

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Book digitized by Google from the library of the University of Michigan and uploaded to the Internet Archive by user tpb.

Topics: equal, angle, angles, hnslcdhygoogic, sides, triangles, perpendicular, triangle, parallel, polygon,...

Source: http://books.google.com/books?id=LqrpGIhgKxwC&oe=UTF-8

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247

Aug 5, 2008
08/08

by
Benjamin Peirce

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Book digitized by Google from the library of Harvard University and uploaded to the Internet Archive by user tpb.

Topics: equal, angle, angles, sides, perpendicular, triangles, triangle, parallel, polygon, plane,...

Source: http://books.google.com/books?id=ISYAAAAAYAAJ&oe=UTF-8

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17

Jun 22, 2017
06/17

by
Bernal, J.

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Topic: Triangularization (Mathematics)Voronoi polygons

All I got done is a one-screen prototype. The final thing would involve a multi-screen base that you disable, then enter inside. There are three shot sizes. When shots of the same size collide they create a bigger shot. (Retrieved from Glorious Trainwrecks .)

Topics: glorious trainwrecks, Klik & Play, Klik of the Month Klub #44, asteroids, base, blue, blue...

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215

Jul 13, 2011
07/11

by
Bret H. Hart

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I once defined this music as Audio Embroidery. The pieces were composed using graph paper; whereupon an area totaling 494 blocks was graphically filled using three (the Triangle pieces) or four (the Circle pieces) symbols; each of which represented a specific note to be sounded to a static rhythm by two performers. One performer would read the score like a Western newspaper (top left to right); the other read the score like a Chinese newspaper (top left to bottom). These compositions were...

Topics: Bret Hart, 494 Polygons, 494, polygons, HipWorks, Audio Embroidery, Instrumental, serial music

14

Topics: Polygons, Polyhedra

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213

Jun 17, 2010
06/10

by
Chapman, D. R.; Larson, H. K.; Scheiber, L. C

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No Abstract Available

Topics: AUSTRALIA, DENSITY (MASS/VOLUME), FLOTATION, POLYGONS, POPULATIONS, TEKTITES

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299

Jun 1, 2011
06/11

by
Chizmadia, Lysa J.; Rubin, Alan E.; Wasson, John T

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Petrographic and mineralogic studies of amoeboid olivine inclusions (AOIs) in CO3 carbonaceous chondrites reveal that they are sensitive indicators of parent-body aqueous and thermal alteration. As the petrologic subtype increases from 3.0 to 3.8, forsteritic olivine (Fa(sub 0-1)) is systematically converted into ferroan olivine (Fa(sub 60-75)). We infer that the Fe, Si and O entered the assemblage along grain boundaries, forming ferroan olivine that filled fractures and voids. As temperatures...

Topics: ELLIPTIC FUNCTIONS, STRUCTURAL VIBRATION, INTEGRALS, FLUID MECHANICS, ANALYTIC FUNCTIONS, POLYGONS,...

This document defines a geometric figure which is called an anti-cylinder, like the cylinder, it has a bottom circle gamma function and a topcircle gamma function' and all common normals of gamma function and gamma function' have the same length c. Figure 2 exhibits a model made by the author of 1 1/2 feet height. Unlike the two circles of a cylinder the circles gamma function and gamma function' are linked, like two consecutive elements in a chain. If made of anodized aluminum tubing and of...

Topics: DTIC Archive, Schoenberg,I J, WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER, *CIRCLES,...

Consider a scenario where a military intelligence ground-operative encounters an array of radars during a reconnaissance mission in enemy territory, where the shape of the array is important to determine its purpose. However, he does not have requisite gadgets to make any accurate positional assessment about the array. He starts noting down the approximate angular direction of each radar from its previous radar position in the array, with respect to the North (say, by observing the Pole Star in...

Topics: DTIC Archive, Mitra, Debasis, FLORIDA INST OF TECH MELBOURNE, *ANGLES, *DIRECTION FINDING,...

This paper introduces the architecture and initial algorithms for Pixel-planes 5, a heterogeneous multi-computer designed both for high-speed polygon and sphere rendering (1M Phong-shaded triangles/second) and for supporting algorithm and application research in interactive 3D graphics. Techniques are described for volume rendering at multiple frames per second, font generation directly from conic, spline descriptions, and rapid calculation of radiosity form factors. The hardware consists of up...

Topics: DTIC Archive, Fuchs, Henry, NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF COMPUTER SCIENCE,...

This paper presents a new method of grouping edges in order to recognize objects. This grouping method succeeds on images of both two- and three-dimensional objects. So that the recognition system can consider first the collections of edges most likely to lead to the correct recognition of objects, we order groups of edges based on the likelihood that a single object produced them. The grouping module estimates this likelihood using the distance that separates edges and their relative...

Topics: DTIC Archive, Jacobs, David W, MASSACHUSETTS INST OF TECH CAMBRIDGE ARTIFICIAL INTELLIGENCE LAB,...

The polygon search problem is the problem of searching for mobile intruders in a simple polygon by a single mobile searcher having various degrees of visibility. This paper considers the open edge variant of the problem in which the given polygon P must be searched without allowing undetected intruders to reach a given edge u, under an additional assumption that any number of intruders can leave and enter P through another edge v at any time. One may view P as representing a corridor with two...

Topics: DTIC Archive, Crass, David, WISCONSIN UNIV-MILWAUKEE DEPT OF ELECTRICAL ENGINEERING AND COMPUTER...

Fast path-planning algorithms are needed for autonomous vehicles and tactical terrain-analysis tools. We explore a new approach using 'optimal-path maps', that give the best path to a goal point from any given start point in cross-country two-dimensional terrain for a moving agent of negligible size. Such maps allow fast point-location algorithms at run-time to categorize the start point according to the behavior of the optimal path to the goal, from which the path can be reconstructed. We...

Topics: DTIC Archive, Alexander, Robert S, NAVAL POSTGRADUATE SCHOOL MONTEREY CA, *OPTIMIZATION, *PATHS,...

Surface formulation of method of moments gives the best results in electromagnetic analysis when geometrical modeling is performed with quadrilateral patches. Quadrilateral modeling, however, can be very difficult. Many structures, e.g. different microwave devices, can be easily modeled using polygonal surfaces. This paper presents general method for conversion of polygonal model into quadrilateral model. Proposed method is illustrated on real microwave filter.

Topics: DTIC Archive, Tasic, Miodrag S, BELGRADE UNIV (YUGOSLAVIA) FACULTY OF ELECTRICAL ENGINEERING,...

In this paper, we give an explicit method for mapping any simply connected surface onto the sphere in a manner which preserves angles. This technique relies on certain conformal mappings from differential geometry. Our method provides a new way to automatically assign texture coordinates to complex undulating surfaces. We demonstrate a finite element method that can be used to apply our mapping technique to a triangulated geometric description of a surface. The technique of texture mapping is...

Topics: DTIC Archive, Haker, Steven, MINNESOTA UNIV MINNEAPOLIS DEPT OF ELECTRICAL AND COMPUTER...

In an information design project at Malardalen University in Sweden a computer based 3-D nautical chart system is designed based on human factors principles of more intuitive navigation in high speeds. In this project dynamic NoGo area polygons is generated based on the draught of the individual ship and the current water level and by doing so space is divided into free and forbidden areas. Based on this an automatic wayfinding method is presented in this paper that will allow vessels to enter...

Topics: DTIC Archive, Porathe, Thomas, MALARDALEN UNIV VASTERAS (SWEDEN), *HUMAN FACTORS ENGINEERING,...

In 1898 J. Kuerschak observed that the area of a regular 12-gon is = 3r square. This is variously generalized in the plane and in space. (Author)

Topics: DTIC Archive, Schoenberg,I J, WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER, *GEOMETRY,...

The POS polyline smoothing algorithm was developed to reduce the needed storage and rendering complexity of polylines by the removal of vertices with two goals in mind. First was to define a single algorithm that would produce a good enough result with varying characteristics, which are user defined. The concept of good enough is built on the trade of time vs. precision, where the best result takes the longest time and the quickest maybe less than desirable form. The second goal was to...

Topics: DTIC Archive, Layne, Geary, NAVAL RESEARCH LAB STENNIS SPACE CENTER MS MARINE GEOSCIENCES DIV,...

In this notebook a collection of new results is presented in computational geometry, which all concern problems of planar geometry. The first problem is that of triangulating a simple n-vertex polygon; we show that this can be done in time 0(nlogn), by first decomposing in time 0(nlogn) the given polygon into a collection of special polygons, called monotone, which can be individually triangulated in time proportional to their numbers of edges. The second result concerns that all-nearest...

Topics: DTIC Archive, Preparata,F P, ILLINOIS UNIV AT URBANA-CHAMPAIGN COORDINATED SCIENCE LAB, *COMPUTERS,...

Scott has recently studied two simple variations on the ordinary histogram, namely the frequency polygon and the average shifted histogram, and found that they are able to compete with for example kernel density estimators in performance while retaining the advantage of being conceptually and computationally simple. The present paper proposes a way of generalizing frequency polygons to d-dimensional space that performs better than Scott's generalization. Expressions for integrated mean squared...

Topics: DTIC Archive, Hjort, Nils L., STANFORD UNIV CA LAB FOR COMPUTATIONAL STATISTICS, *ERROR ANALYSIS,...

This report documents a distributable, device-independent vector graphics system developed by ISI for the Defense Advanced Research Projects Agency. It describes the system architecture, communications elements, and a phased implementation strategy. The system supports graphics-based command and control applications in distributed computational environments such as the ARPANET. The system has been in use at ISI and at the Naval Ocean Systems Center (NOSC) in the Advanced Command and Control...

Topics: DTIC Archive, Bisbey, II, Richard, UNIVERSITY OF SOUTHERN CALIFORNIA MARINA DEL REY INFORMATION...

A parallel C implementation of the marching cubes method is discussed. The input data for the code consists of a variation of the unformatted PLOT3D grid and solution files. PLOT3D files can define an irregularly or regularly spaced mesh and the associated scalars given by v(x,y, z), F(x,y,z), and S sub n = F(x,y,z), respectively. The output is a collection of three-sided polygons defining a constant value of F(x,y,z), and a second scalar which will be mapped onto this surface. The output is...

Topics: DTIC Archive, Burke, Kathy A, COMPUTER SCIENCES CORP FALLS CHURCH VA, *INPUT OUTPUT PROCESSING,...

Between 1987 and 1992, ERDAS, Inc., and Gilmore Aerospace Corporation developed a prototype expert system for the update of Digital Feature Analysis Data (DFAD) based on multispectral imagery and a number of commonly available Geographic Information System (GIS) layers. A method was developed by which ERDAS GIS Modeling tools were used to simulate and validate decision rules that were then downloaded to the Ada Based Expert System Testbed (ABEST) for execution. ERDAS developed data acquisition...

Topics: DTIC Archive, Jordan, Lawrie, ERDAS INC ATLANTA GA, *PROTOTYPES, *EXPERT SYSTEMS, *DIGITAL MAPS,...

This paper presents all possible isomerizations involving the 34 combinatorially distinct seven-vertex polyhedra. Such isomerizations are expressed in the form P sub 1 yields P sub 2 yields P sub 3 in which P sub 1 and P sub 3 have the same number of edges and the intermediate polyhedron P sub 2 has fewer edges than P sub 1 or P sub 3. Isomerizations of this type are regarded as degenerate if P sub 1 is combinatorially equivalent to P sub 3 and planar if P sub 2 is a planar polygon. Non-planar...

Topics: DTIC Archive, King,R B, GEORGIA UNIV ATHENS DEPT OF CHEMISTRY, *ISOMERIZATION, *MOLECULAR...

In this paper, we propose and analyze two algorithms to monitor an environmental boundary with mobile sensors. The objective is to optimally approximate the boundary with a polygon. In the first scenario the mobile sensors know the boundary and the approximating polygon is defined by the sensors' positions. In the second scenario the mobile sensors rely only on sensed local information to position some interpolation points and define an approximating polygon. For both scenarios we design...

Topics: DTIC Archive, Susca, Sara, CALIFORNIA UNIV SANTA BARBARA, *ROBOTICS, *DETECTORS, *MONITORING,...

Consider the existence of regular solutions to the boundary value problem div U = f on a plane polygonal domain Omega with the Dirichlet boundary condition U = g on del Omega. We formulate simultaneously necessary and sufficient conditions on f and g in order that a solution U exist in the Sobolev space W (over s+1 to p) (Omega). In addition to the obvious regularity and integral conditions these consist of at most one compatibility condition at each vertex of the polygon. In the special case...

Topics: DTIC Archive, Arnold, Douglas N, MARYLAND UNIV BALTIMORE DEPT OF MATHEMATICS, *BOUNDARY VALUE...

Three hundred sixty-eight geologic maps of 7 1/2-minute quadrangles in Tennessee were converted to geographic information system (GIS) coverages. The procedure used was documented and a list was made of the quadrangles included in the coverages. Maps were converted to GIS coverages by making film copies of scribecoats of the maps. The film copies were scanned, vectorized, and written into a generate format. Coverage polygons were tagged with symbols to identify geologic units, and coverage...

Topics: DTIC Archive, Connell, Joseph F, DEPARTMENT OF THE INTERIOR WASHINGTON DC, *GEOLOGY, *MAPPING,...

In this notebook we present a collection of three new results in planar computational geometry. The first problem is to test a given n-vertex simple polygon for monotonicity; this problem can be optimally solved in time theta(n). The second result is an improved algorithm for the rectangle enclosure problem; this algorithm improves over an existing one by using optimal space theta(n). Finally, the third result is the construction, in time 0(nlogn), of the shortest path between two points in the...

Topics: DTIC Archive, Preparata,F P, ILLINOIS UNIV AT URBANA APPLIED COMPUTATION THEORY GROUP,...

This paper applies the technique of the h-p version to the boundary element method for boundary value problems on non-smooth, plane domains with piecewise analytic boundary and data. The exponential rate of convergence of the boundary element Galerkin solution is proven when a geometric mesh refinement towards the vertices is used. (KR)

Topics: DTIC Archive, Babuska, I, MARYLAND UNIV COLLEGE PARK INST FOR PHYSICAL SCIENCE AND TECHNOLOGY,...

In this paper, we will give an h-version finite element method for a two dimensional nonlinear elasto-plasticity problem. A family of admissible constitutive laws based on the so-called gauge function method is introduced first, and then a high order h-version semi-discretization scheme is presented . The existence and uniqueness of the solution for the semi-discrete problem are guaranteed by using some special properties of the constitutive law, and finally we will show that as the maximum...

Topics: DTIC Archive, Li, Y, MARYLAND UNIV COLLEGE PARK INST FOR PHYSICAL SCIENCE AND TECHNOLOGY, *FINITE...

The ability to make computer images more realistic is becoming more important as the hardware for producing such images is becoming less expensive and hence more available. The key to producing realistic images lies in the algorithms that can take full advantage of the hardware to produce them. In this study, we look at a prototype of one ray tracer. Ray tracing, in combination with a global illumination model, currently provides the most realistic images that can be generated on general...

Topics: DTIC Archive, Smith, Paul G, NAVAL POSTGRADUATE SCHOOL MONTEREY CA, *MODELS, *IMAGES, *SHADOWS,...

A method is presented to extract linear terrain features from Synthetic Aperture Radar imagery. An input radar image is smoothed with an edge- preserving smoothing operation. Edge detection is performed using a Sobel operator, and both the magnitude and directional images are computed. The edges are then strengthened using several iterations of a relaxation operation in which both the magnitude image and the directional image are updated with each iteration. The output of the relaxation...

Topics: DTIC Archive, Hevenor, Richard A, ARMY ENGINEER TOPOGRAPHIC LABS FORT BELVOIR VA, *ALGORITHMS,...

The classical error estimates for the h-version of the finite element method are extended for the h-p version. The estimates are expressed as explicit functions of h and p are shown to be optimal. The estimates are given for the case where the solution u (H sub k and the case when u has singularities at the corners of the domain. (Author)

Topics: DTIC Archive, Babuska,Ivo, MARYLAND UNIV BALTIMORE COUNTY BALTIMORE DEPT OF MATHEMATICS, *FINITE...

We explain and describe diffraction from polygonal apertures over a wide range of sizes and observation distances. In the first case considered, a small square aperture (2a X 2a, ka 1, where k = 2pi/lambda is the wavenumber) in a perfectly conducting plane screen of vanishing thickness diffracts a normally incident, linear polarized, monochromatic plane wave. Within the vector framework of Maxwell's equations, we hypothesize a solution for the dominant component of the electric field....

Topics: DTIC Archive, English, R E , Jr, ROCHESTER UNIV NY INST OF OPTICS, *DIFFRACTION, *ELECTRIC FIELDS,...

This paper examines a method of manipulating data in grid cell spatial data management systems such as Geographic Information Systems (GIS) and digital cartographic systems. While scan line methods have advantages when used only in traditional GIS operations such as manipulation of region polygons (binary overlays), much of this paper discusses digital imagery, digitized map backgrounds, and other types of 'pictorial' or multibit data. This is because the integration of these kinds of data with...

Topics: DTIC Archive, McDonnell, Michael, ARMY ENGINEER TOPOGRAPHIC LABS FORT BELVOIR VA, *DATA BASES,...

US Army Night Vision and Electronic Sensors Directorate (NVESD) has recently developed a process for generating polygonal target models with attributions suitable for integration with thermal modeling code for use with its infrared sensor simulation Paint the Night (PTN). This paper will describe the process for generating those models from high-resolution Combinatorial Solid Geometry (CSG) models and close-up infrared sensor imagery. It will discuss the method of encoding material attributions...

Topics: DTIC Archive, Miller, Brian, Kang, Robin, ARMY COMMUNICATIONS AND ELECTRONICS MATERIEL READINESS...

In this paper, we deal with the monotonicity of curvature problem for Bezier-de Casteljau curves. We focus more particularly on the cubic case. A condition about decreasing curvature at the origin of a cubic curve is given so that it implies decreasing curvature at every point. The corresponding cubics are determined by their control polygon.

Topics: DTIC Archive, Fiorot, Jean Charles, Schiavon, Laurent, UNIVERSITE DE VALENCIENNES ET DU...

SKETCH is a FORTRAN program which is intended to provide quick and painless generation of engineering geometry. The program will utilize any of a number of Tektronix storage tube terminals, including the 4010 and the 4014. Input devices include the terminal keyboard, cross hair thumbwheels, Tek 4953 and 4963 digitizing tablets, and an experimental mouse developed at LSU. The objective of the program is to automatically convert two-dimensional 'picture' data into a rich data base consisting of...

Topics: DTIC Archive, Brewer,John A , III, ARMY ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG MS,...

An outline is given of the development history of Royal Aircraft Establishment(RAE) carbon fibre reinforced plastics. Initially, development was inhibited by poor interlaminar shear strength. However, composite properties have improved since the advent of various surface treatments derived by the fibre producers. Present work indicates certain criteria by which resins are selected for use as a matrix with the two available types of RAE fibre. These are more critical for filament wound...

Topics: DTIC Archive, Jones, M. W., IMPERIAL METAL INDUSTRIES LTD KIDDERMINSTER (UNITED KINGDOM)...

The paper surveys techniques for filling in n-sided regions, where n > 4. The two major classes of methods examined are: (1) to fill in the hole with 4 and/or 3 sided patches, and (2) to create a single surface. The multi-patch approaches differ in terms of the degree of the patches and the cross-patch continuity. The single surface approaches are either rational surfaces (which can be expressed in terms of base points) or non-rational, both cases having a number of variants.

Topics: DTIC Archive, Malraison, Pierre, SPATIAL TECHNOLOGY INC BOULDER CO, *APPROXIMATION(MATHEMATICS),...

The focus of this thesis is performing walkthroughs of urban environments in real-time. This encompasses the environment both inside and outside the building, whereby a user can traverse the external virtual world and then enter any building and move throughout the interior. While inside the building, the user can see the exterior world via any windows present. The transition from one environment to the other is transparent to the user. The 2D terrain file used as source data is converted and...

Topics: DTIC Archive, Boone, Mark R, NAVAL POSTGRADUATE SCHOOL MONTEREY CA, *REAL TIME, *TERRAIN, *WAR...